Adaptive mesh refinement generally serves to increase computational efficiency without compromising the accuracy of the numerical solution significantly. However it is an open question in which regions the spatial resolution can actually be coarsened without affecting the accuracy of the result significantly. Another open question is the following: does an adaptive computation simulate large scale features of the flow more accurately than a uniform simulation when both use the same CPU time? These questions are investigated in the case of a 2D dry warm air bubble with the help of a recently developed adaptive discontinuous Galerkin model.

A method is introduced which allows one to compare the accuracy between different choices of refinement regions even in a case when the exact solution is not known. Essentially this is done by comparing features of the solution that are strongly sensitive to spatial resolution. The additional error by using adaptivity is smaller than 1% of the total numerical error if the average number of elements used for the adaptive simulation is about 50% smaller than the number used for the simulation with the uniform fine-resolution grid. Correspondingly the adaptive simulation is almost two times faster than the uniform simulation. Furthermore the adaptive simulation is more accurate than a uniform simulation when both use the same CPU time.

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